Multiparameter quantum enveloping algebras (Q1919560)

Let \(A=A(p,q)\) be the multiparameter quantum \(n\) by \(n\) matrix algebra, \(U\) its quantum enveloping algebra. Here \(p=(p_{ij})\), \(p_{ij}\), \(q\) scalar and \(q\) not a root of unity. The authors prove a Poincaré-Birkhoff-Witt theorem for \(U\), and establish a presentation by generators and relations. Some of these results were known earlier, but the authors' methods here involve Hopf algebra techniques, namely a description of the coradical filtration and cocycle-twisted adjoint actions.